Once subtracted Roy-like dispersion relations and a precise analysis of pion-pion scattering data (original) (raw)
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Forward dispersion relations and Roy equations in ππ scattering
The European Physical Journal A, 2007
We review results of an analysis of ππ interactions in S, P and D waves for two-pion effective mass from threshold to about 1.4 GeV. In particular we show a recent improvement of this analysis above the KK threshold using more data for phase shifts and including the S0 wave inelasticity from ππ → KK. In addition, we have improved the fit to the f2(1270) resonance and used a more flexible P wave parametrization above the KK threshold and included an estimation of the D2 wave inelasticity. The better accuracy thus achieved also required a refinement of the Regge analysis above 1.42 GeV. We have checked that the ππ scattering amplitudes obtained in this approach satisfy remarkably well forward dispersion relations and Roy's equations.
Precise analysis of ππ scattering data from Roy equations and forward dispersion relations
AIP Conference Proceedings, 2008
We reviewo ur recent analysis of ππ scattering data in terms of Roye quations and Forward Dispersion Relations, and present some preliminary results in terms of anew set of oncesubtracted coupled equations for partial waves. The first analysis consists of independent fits to the different ππ channels that satisfies rather well the dispersive representation. In the second analysis we constrain the fit with the dispersion relations. The latter provides av ery precise and model independent description of data using just analyticity,causality and crossing.
Physical Review D, 2008
We complete and improve the fits to experimental ππ scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity requirements, in the form of partial wave analyticity at low energies, forward dispersion relations (FDR) at all energies, and Roy equations belowKK threshold; the first by construction, the last two, inside experimental errors. Then we repeat the fits including as constraints FDR and Roy equations. The ensuing central values of the various scattering amplitudes verify very accurately FDR and, especially, Roy equations, and change very little from what we found by just fitting data, with the exception of the D2 wave phase shift, for which one parameter moves by 1.5 σ. These improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test various physical relations. We also present a list of low energy parameters and other observables. In particular, we find a (0) 0
Unsubtracted Pion-Pion Dispersion Relation
Physical Review, 1967
The de Alfaro-Fubini-Furlan-Rossetti assumption on the rapid falloff of amplitudes corresponding to pure 1-2, /-channel exchange is applied to pion-pion forward dispersion relations, and a sum rule is obtained for the pion-pion scattering lengths. The sum rule is fairly well satisfied using the p, f, and low-energy s-wave contributions; but the inclusion of the recently discovered gi resonance requires the existence of at least one new 7=0 resonance to satisfy the sum rule.
Pion-pion scattering amplitude. II. Improved analysis above K¯K threshold
Physical Review D, 2006
We improve, in the energy region betweenKK threshold and ∼ 1.4 GeV, the energy-dependent phase shift analysis of ππ scattering presented in a previous paper. For the S0 wave we have included more data aboveKK threshold and we have taken into account systematically the elasticity data on the reaction ππ → KK. We here made a coupled channel fit. For the D0 wave we have considered information on low energy parameters, and imposed a better fit to the f2 resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for s 1/2 ≥ 1.42 GeV, which we also carry out. We show that this more realistic input produces ππ scattering amplitudes that satisfy better forward dispersion relations, particularly for π 0 π 0 scattering.
Physical Review D, 2006
We improve, in the energy region betweenKK threshold and ∼ 1.4 GeV, the energy-dependent phase shift analysis of ππ scattering presented in a previous paper. For the S0 wave we have included more data aboveKK threshold and we have taken into account systematically the elasticity data on the reaction ππ → KK. We here made a coupled channel fit. For the D0 wave we have considered information on low energy parameters, and imposed a better fit to the f2 resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for s 1/2 ≥ 1.42 GeV, which we also carry out. We show that this more realistic input produces ππ scattering amplitudes that satisfy better forward dispersion relations, particularly for π 0 π 0 scattering.
Nuclear Physics B - Proceedings Supplements, 2009
This talk is dedicated to the memory of Paco Ynduráin, the original speaker in the conference. After a short account of his scientific career, we briefly review our ongoing collaboration to determine precisely the ππ scattering amplitude including the most recent data by means of Forward Dispersion Relations and Roy Equations. A remarkable improvement in precision over the intermediate energy region is obtained by using once-subtracted Roy Equations in addition to the standard twice-subtracted ones.
Regge analysis of pion-pion (and pion-kaon) scattering for energy s1/2>1.4 GeV
Physical Review D, 2004
We perform a detailed Regge analysis of N N , πN , KN , ππ and πK scattering. From it, we find expressions that represent the ππ scattering amplitudes with an accuracy of a few percent, for exchange of isospin zero, and ∼ 15% for exchange of isospin 1, and this for energies s 1/2 > 1.4 GeV and for momentum transfers |t| 1/2 < ∼ 0.4 GeV. These Regge formulas are perfectly compatible with the low energy (s 1/2 ∼ 1.4 GeV) scattering amplitudes deduced from ππ phase shift analyses as well as with higher energy (s 1/2 > ∼ 1.4 GeV) experimental ππ cross sections. They are also compatible with N N , KN and πN experimental cross sections using factorization, a property that we check with great precision. This contrasts with results from current phase shift analyses of the ππ scattering amplitude which bear little resemblance to reality in the region 1.4 < s 1/2 < 2 GeV, as they are not well defined and increasingly violate a number of physical requirements when the energy grows. πK scattering is also considered, and we present a Regge analysis for these processes valid for energies s 1/2 > 1.7 GeV. As a byproduct of our analysis we present also a fit of N N , πN and KN cross sections valid from c.m. kinetic energy E kin ≃ 1 GeV to multi TeV energies. Typeset with P H ys Ma T E X-regge analysis of pion-pion (and pion kaon) scattering
The pion-pion scattering amplitude
2004
We obtain reliable ππ scattering amplitudes consistent with experimental data, both at low and high energies, and fulfilling appropriate analyticity properties. We do this by first fitting experimental low energy (s^1/2≤1.42 GeV) phase shifts and inelasticities with expressions that incorporate analyticity and unitarity. In particular, for the S wave with isospin 0, we discuss in detail several sets of experimental data. This provides low energy partial wave amplitudes that summarize the known experimental information. Then, we impose Regge behaviour as follows from factorization and experimental data for the imaginary parts of the scattering amplitudes at higher energy, and check fulfillment of dispersion relations up to 0.925 GeV. This allows us to improve our fits. The ensuing ππ scattering amplitudes are then shown to verify dispersion relations up to 1.42 GeV, as well as s - t - u crossing sum rules and other consistency conditions. The improved parametrizations therefore provi...